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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Then (<a href="" class="xref" data-knowl="./knowl/eq7_2.html" title="Equation 6.1.2">(6.1.2)</a>) becomes</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq7_2.html ./knowl/eq7_4.html">
\begin{equation}
{\bf x}^{\prime}={\bf P}(t) {\bf x}+{\bf g}(t).\tag{6.1.4}
\end{equation}
</div>
<p class="continuation">If a vector</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq7_2.html ./knowl/eq7_4.html">
\begin{equation*}
{\bf x}=\vec{\phi}(t)=\left(
\begin{array}{c}
\phi_1(t)\\
\phi_2(t)\\
\vdots\\
\phi_n(t)
\end{array}
\right)
\end{equation*}
</div>
<p class="continuation">satisfies (<a href="" class="xref" data-knowl="./knowl/eq7_4.html" title="Equation 6.1.4">(6.1.4)</a>), it is called a solution. We denote the solutions as</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq7_2.html ./knowl/eq7_4.html">
\begin{equation*}
{\bf x}^{(1)}(t)=\left(
\begin{array}{c}
x_1^{(1)}(t)\\
x_2^{(1)}(t)\\
\cdots\\
x_n^{(1)}(t)\\
\end{array}
\right),\cdots, 
{\bf x}^{(n)}(t)=\left(
\begin{array}{c}
x_1^{(n)}(t)\\
x_2^{(n)}(t)\\
\cdots\\
x_n^{(n)}(t)\\
\end{array}
\right).
\end{equation*}
</div>
<span class="incontext"><a href="sec6_1.html#p-251" class="internal">in-context</a></span>
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